No, you don't need to file a US tax return just to report this 1099-R.
The code G in box 7 means that the retirement account was directly rolled over to another retirement account, so it's not taxable.
You won't get another 1099-R until you actually distribute the money in the account, or move it to another retirement account.
You will get a Form 5498 every year, but you don't report that on your tax return. Form 5498 just lets you know the year end value of the account and whether you are required to take a distribution. Just keep them with your tax records.
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